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A multistage reduction technique for feedback stabilizing distributed time-lag systems. (English) Zbl 0629.93046

This paper presents a method which can be used to stabilize a system with state and control delays of the form:

x ˙= -h 0 dα(s)x(t+s)+ -h 0 dβ(s)u(t+s)·

A preliminary requirement for this method is that the equation A= -h 0 exp(As)dα(s) can be solved with respect to the unknown matrix A. Let Γ be the set of the matrices A which solve this last equation. Then, it is proved that σ (A) is contained in the spectrum of the delay system for each AΓ. Moreover, a special transformation can be applied to the pairs (x,u) (which solve the delay system) so that the transformed pair is solution of an ordinary differential equation. It is shown, under suitable assumptions, that a feedback which stabilizes this last equation can be used for the task of stabilizing the delay system.

Reviewer: L.Pandolfi

MSC:
93D15Stabilization of systems by feedback
34K35Functional-differential equations connected with control problems
93C05Linear control systems
93B17System transformation
93B55Pole and zero placement problems
93C25Control systems in abstract spaces